Division Mentally

I’ve been reading about mental calculus for a while, but I’ve recently realized that I’ve never found anything teaching how to do mental division without resorting to the traditional method. Do you know any method of division? Any different from the traditional one used in schools?

If your unit digit is 9, you can use the tenths digit + 1 and simply carry over the remainder.

12/19 for example… use 2 as 19+1=20

12/2=6
6/2= 3
3/2=1 remainder 1

So far you got: .631 now put the remainder to the left of the last digit you calculated to get 11

11/2=5 remainder 1

Now you got: .6315 again you put the remainder left to get 15

15/2=7 remainder 1

Now you got: .63157 put the remainder left to get 17

17/2=8 remainder 1

18/2=9

9/2=4 remainder 1

Now you got: .63157894 and again the remainder to the left to get 14

14/2=7 which is the same as denominator (19) - numerator (12) i.e. 7 and since we dividing by a prime number you can now simply use the 9 compliments to fill the rest.

631578947
368421052 
999999999

12/19= .631578947368421052 (repeating)

If you had 15/29 you’d use 3

15/3=5
5/3=1 remainder 2
21/3=7
7/3=2 remainder 1
12/3=4
4/3 …etc. hope you get the idea.

Next one is 1 for so far: .517241 and again you can stop at 29-15=14 because 29 is also prime and fill up with 9

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Very interesting this method!

You could also do it right-to-left instead of left-to-right and essentially turn it into a multiplication. :wink:

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You might want to google vedic division.

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I have written a lot on this forum about mental division.
Examples here:















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